Question

can someone explain how to MULTIPLY IRRATIONAL NUMBERS USING THE LCM METHOD.
FOR EG. THE ATTACHED QUESTION IS DONE USING THE LCM METHOD SO CAN SOMEONE EXPLAIN IT OR SEND ME A LINK WHERE I CAN LEARN IT BY MYSELF...
THANKS ALOT
I HAVE A TEST TOMORROW SO PLZ SEND ME THE ANSWER ASAP..

Answer 1

let's take an example of
$\sqrt[3]{5} \times \sqrt[2]{2}$
given in the image

power of 5 is 1/3 i.e
${5}^{ \frac{1}{3} }$
power of 2 is 1/2 i.e
${2}^{ \frac{1}{2} }$
LCM of 2 and 3 is 6

so, make the denominator of powers of both numbers to 6

first let's take 5, it's power is 1/3
to make denominator as 6, multiple by 2/2 i.e,
$\frac{1}{3} \times \frac{2}{2} = \frac{2}{6}$
now power of 5 is 2/6 i.e
${5}^{ \frac{2}{6} } = \sqrt[6]{ {5}^{2} }$
now let's take 2, it's power is 1/2
to make denominator as 6, multiple by 3/3 i.e
$\frac{1}{2} \times \frac{3}{3} = \frac{3}{6}$
now power of 2 is 3/6 i.e
$\sqrt[6]{ {2}^{3} }$
so,
$multiply\: of \: \sqrt[6]{ {5}^{2} } \: and \: \sqrt[6]{ {2}^{3} } \\ = \sqrt[6]{25} \times \sqrt[6]{ 8 } \\ = \sqrt[6]{25 \times 8} \\ = \sqrt[6]{200}$
note: if square root power are equal then multiple of two numbers can be done